Question

In a class there are 15 boys and 12 girls. The teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make the selection?

Answer 1

Hint: We will select 1 boy from 15 boys and we can select any of the boys. Hence 15 ways will be there to select a boy. Similarly we will select 1 girl from 12 girls and we can select any of the girls. Hence 12 ways will be there to select a girl.

Complete step-by-step answer:
Here the teacher has to perform two operations as mentioned in the question. First operation is to select 1 boy out of 15 boys and second operation is to select 1 girl out of 12 girls.
Now the first operation can be done in 15 ways as there is no restriction and similarly the second operation can be done in 12 ways as there is again no restriction.
So from the fundamental principle of multiplication,
the required number of ways \[=15\times 12=180\].
Hence, the teacher can make the selection of 1 boy and 1 girl in 180 ways.

Note: Students can make a mistake in finding the total number of ways to select 1 boy and 1 girl from 15 boys and 12 girls by adding all the ways and doing this they will get the answer as 27, hence remembering the concept of fundamental principle of multiplication is the key here. The fundamental counting principle (also called the multiplication rule) is a way to figure out the number of outcomes in a probability problem. Basically, we multiply the events together to get the total number of outcomes.